\chapter[Differential Equations \\ \textnormal{\emph{Lectured in Michaelmas \oldstylenums{2020} by \textsc{Dr.\ J.\ R.\ Taylor}}}]{Differential Equations}
\emph{\Large Lectured in Michaelmas \oldstylenums{2020} by \textsc{Dr.\ J.\ R.\ Taylor}}

A differential equation is an equation involving one or more unknown functions and their derivatives.
These equations arise in many fields of study, such as physics and biology.
In this course, we explore many different ways to solve some common types of differential equations.

In many cases, it is not possible to solve differential equations, so it is important to classify various cases that we can solve, and explore them in depth.
Heuristically, a differential equation is often easier to solve if it involves fewer variables, and if the derivatives involved have a lower order.
First, we will study differential equations in only one variable: the `ordinary' differential equations.
Towards the end of the course, we study `partial' differential equations, which can involve more than one variable.

\subfile{../../ia/de/main.tex}
